平行平板流动腔中脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一。大多数研究者主要对定常层流情形进行研究。考虑到通常采用的矩形平行平板流动腔内的流动属小雷诺数流动，本文用雷诺数作为摄动参数求出矩形平行平板流动腔内的层流脉动流的摄动解，给出腔内流速和腔室底部切应力的0级、I级、Ⅱ级近似计算公式。数值计算结果及其与Fourier解的比较表明，在脉动流条件下，对于人们常用的流动腔几何尺寸，近似公式具有相当高的精度，特别是0级近似公式（即准定常公式）适用的雷诺数范围更大。这为在脉动流情况下平行平板流动腔切应力的简便计算方法提供了理论依据。

A PERTURBATION SOLUTION OF PULSATILE FLOW IN THE PARALLEL-PLATE FLOW CHAMBER

The parallel-plate flow chamber(PPFC)with rectangular shape,of which the height is far smaller than its own length and width,is one of the main apparatus for in vitro studies of the mechanical behavior of cultured en-dothelial cells undergoing shear stress.The PPFCs are usually utilized to study the cells'mechanical behavior under steady flow condition.Considering that the Reynolds numbers of the flows in the usually used PPFCs are small,a perturbation solution of laminar pulsatile flows in the PPFCs is presented using Reynolds number as perturbation parameter.The0-order,first-order,second-order approximate calculation formulas of the velocities in the PPFCs and the shear stress at the bottom of the PPFCs are given in this paper.The calculated numeri-cal results and the comparison between the perturbation solution and the Fourier solution demonstrate that,the approximate formulas are highly precise for various commonly used flow parameters and geometrical dimensions of the PPFCs.In particular,the0-order approximate formula,the quasi-steady formula,is much more appropri-ate to the pulsatile flow with higher Reynolds number,which provides a practical method for the calculation of the shear stress in the PPFC under pulsatile flow condition.